Question 369083: (1). Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:
(A) Ho:u >/_81 and,Ha:u<81, a = 0.05
(> with line under)
(B) Ho:u= 45 and Ha:u (=/)45, a = 0.10
(C)Ho:u 88, a = 0.01
(< with line under)
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
The critical regions appropriate to be used to test the null hypothesis will
depend on the parameters set by Ho & Ha. In general:
a a/2 crtical regions
90% 10 5% z <-1.645 z >+1.645
95% 5 2.50% z <-1.96 z >+1.96
98% 2 1% z <-2.33 z >+2.33
99% 2 0.50% z<-2.575 z >+2.575
For example when testing the Ho, the following would be used and will result
in a negative or positive number depending on the value of X used in the
test statistic = 
(A) Ho: u ≥ 81 and Ha: u <81, a = 0.05
this will result in a negative test statistic as the test value used for X < u
therefore, the critical region would be z < -1.96
(B) Ho: u= 45 and Ha: u<45 or>45, a = 0.10
The result for a test statistic here may be neg or positive depending on test value of X used
therefore, the critical regions would be z< -1.645 or z > +1.64
(C)Ho: u ≤ 88, a = 0.01
The result for this test statistic will be positve because test value used for X > u
therefore, the critical regions would be z > +2.33
Hope this helps to clear this up.
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